TSTP Solution File: SEU186+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:03 EDT 2022
% Result : Theorem 1.93s 1.46s
% Output : Proof 1.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 10:09:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 1.93/1.46 % SZS status Theorem
% 1.93/1.46 % SZS output start Proof
% 1.93/1.46 tff(empty_type, type, (
% 1.93/1.46 empty: $i > $o)).
% 1.93/1.46 tff(tptp_fun_A_8_type, type, (
% 1.93/1.46 tptp_fun_A_8: $i)).
% 1.93/1.46 tff(in_type, type, (
% 1.93/1.46 in: ( $i * $i ) > $o)).
% 1.93/1.46 tff(tptp_fun_B_3_type, type, (
% 1.93/1.46 tptp_fun_B_3: $i > $i)).
% 1.93/1.46 tff(ordered_pair_type, type, (
% 1.93/1.46 ordered_pair: ( $i * $i ) > $i)).
% 1.93/1.46 tff(tptp_fun_D_0_type, type, (
% 1.93/1.46 tptp_fun_D_0: $i > $i)).
% 1.93/1.46 tff(tptp_fun_C_1_type, type, (
% 1.93/1.46 tptp_fun_C_1: $i > $i)).
% 1.93/1.46 tff(relation_type, type, (
% 1.93/1.46 relation: $i > $o)).
% 1.93/1.46 tff(tptp_fun_B_2_type, type, (
% 1.93/1.46 tptp_fun_B_2: $i > $i)).
% 1.93/1.46 tff(empty_set_type, type, (
% 1.93/1.46 empty_set: $i)).
% 1.93/1.46 tff(element_type, type, (
% 1.93/1.46 element: ( $i * $i ) > $o)).
% 1.93/1.46 tff(1,assumption,(in(tptp_fun_B_3(A!8), A!8)), introduced(assumption)).
% 1.93/1.46 tff(2,plain,
% 1.93/1.46 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(3,plain,
% 1.93/1.46 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[2])).
% 1.93/1.46 tff(4,plain,
% 1.93/1.46 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(5,plain,
% 1.93/1.46 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[4])).
% 1.93/1.46 tff(6,plain,
% 1.93/1.46 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(transitivity,[status(thm)],[5, 3])).
% 1.93/1.46 tff(7,plain,
% 1.93/1.46 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))), rewrite((relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(8,plain,
% 1.93/1.46 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[7])).
% 1.93/1.46 tff(9,plain,
% 1.93/1.46 (^[A: $i] : rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))),
% 1.93/1.46 inference(bind,[status(th)],[])).
% 1.93/1.46 tff(10,plain,
% 1.93/1.46 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 1.93/1.46 inference(quant_intro,[status(thm)],[9])).
% 1.93/1.46 tff(11,plain,
% 1.93/1.46 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(12,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_1')).
% 1.93/1.46 tff(13,plain,
% 1.93/1.46 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.93/1.46 tff(14,plain,(
% 1.93/1.46 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (~(~(B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 1.93/1.46 inference(skolemize,[status(sab)],[13])).
% 1.93/1.46 tff(15,plain,
% 1.93/1.46 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.93/1.46 tff(16,plain,
% 1.93/1.46 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[15, 8])).
% 1.93/1.46 tff(17,plain,
% 1.93/1.46 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[16, 6])).
% 1.93/1.46 tff(18,plain,
% 1.93/1.46 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D))))))))))),
% 1.93/1.46 inference(quant_inst,[status(thm)],[])).
% 1.93/1.46 tff(19,plain,
% 1.93/1.46 (~((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D)))))))))),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[18, 17])).
% 1.93/1.46 tff(20,plain,
% 1.93/1.46 (((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D))))))))) | ((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))),
% 1.93/1.46 inference(tautology,[status(thm)],[])).
% 1.93/1.46 tff(21,plain,
% 1.93/1.46 ((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 1.93/1.46 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.93/1.46 tff(22,plain,
% 1.93/1.46 (((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & (~(~relation(A!8)))) <=> ((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & relation(A!8))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(23,plain,
% 1.93/1.46 ((~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))) <=> (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A))))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(24,plain,
% 1.93/1.46 ((~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A))))),
% 1.93/1.46 inference(rewrite,[status(thm)],[])).
% 1.93/1.46 tff(25,axiom,(~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_relat_1')).
% 1.93/1.46 tff(26,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.93/1.46 tff(27,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.93/1.46 tff(28,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.93/1.46 tff(29,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[28, 23])).
% 1.93/1.46 tff(30,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[29, 23])).
% 1.93/1.46 tff(31,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.93/1.46 tff(32,plain,
% 1.93/1.46 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 1.93/1.46 inference(modus_ponens,[status(thm)],[31, 23])).
% 1.93/1.46 tff(33,plain,
% 1.93/1.46 ((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & relation(A!8)),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[32, 22])).
% 1.93/1.47 tff(34,plain,
% 1.93/1.47 (relation(A!8)),
% 1.93/1.47 inference(and_elim,[status(thm)],[33])).
% 1.93/1.47 tff(35,plain,
% 1.93/1.47 ((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 1.93/1.47 inference(tautology,[status(thm)],[])).
% 1.93/1.47 tff(36,plain,
% 1.93/1.47 ((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 1.93/1.47 tff(37,plain,
% 1.93/1.47 (![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[36, 21])).
% 1.93/1.47 tff(38,plain,
% 1.93/1.47 (((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))) <=> ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(39,plain,
% 1.93/1.47 ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))),
% 1.93/1.47 inference(quant_inst,[status(thm)],[])).
% 1.93/1.47 tff(40,plain,
% 1.93/1.47 ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.93/1.47 tff(41,plain,
% 1.93/1.47 (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[40, 37, 1])).
% 1.93/1.47 tff(42,plain,
% 1.93/1.47 (ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))) = tptp_fun_B_3(A!8)),
% 1.93/1.47 inference(symmetry,[status(thm)],[41])).
% 1.93/1.47 tff(43,plain,
% 1.93/1.47 (in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8) <=> in(tptp_fun_B_3(A!8), A!8)),
% 1.93/1.47 inference(monotonicity,[status(thm)],[42])).
% 1.93/1.47 tff(44,plain,
% 1.93/1.47 (in(tptp_fun_B_3(A!8), A!8) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 1.93/1.47 inference(symmetry,[status(thm)],[43])).
% 1.93/1.47 tff(45,plain,
% 1.93/1.47 (in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[1, 44])).
% 1.93/1.47 tff(46,plain,
% 1.93/1.47 (^[B: $i, C: $i] : refl((~in(ordered_pair(B, C), A!8)) <=> (~in(ordered_pair(B, C), A!8)))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(47,plain,
% 1.93/1.47 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) <=> ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[46])).
% 1.93/1.47 tff(48,plain,
% 1.93/1.47 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 1.93/1.47 inference(and_elim,[status(thm)],[33])).
% 1.93/1.47 tff(49,plain,
% 1.93/1.47 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.93/1.47 tff(50,plain,
% 1.93/1.47 ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8))),
% 1.93/1.47 inference(quant_inst,[status(thm)],[])).
% 1.93/1.47 tff(51,plain,
% 1.93/1.47 (~in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[50, 49])).
% 1.93/1.47 tff(52,plain,
% 1.93/1.47 ($false),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[51, 45])).
% 1.93/1.47 tff(53,plain,(~in(tptp_fun_B_3(A!8), A!8)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.47 tff(54,plain,
% 1.93/1.47 (![A: $i] : ?[B: $i] : element(B, A) <=> ![A: $i] : ?[B: $i] : element(B, A)),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(55,axiom,(![A: $i] : ?[B: $i] : element(B, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m1_subset_1')).
% 1.93/1.47 tff(56,plain,
% 1.93/1.47 (![A: $i] : ?[B: $i] : element(B, A)),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.93/1.47 tff(57,plain,(
% 1.93/1.47 ![A: $i] : element(tptp_fun_B_3(A), A)),
% 1.93/1.47 inference(skolemize,[status(sab)],[56])).
% 1.93/1.47 tff(58,plain,
% 1.93/1.47 ((~![A: $i] : element(tptp_fun_B_3(A), A)) | element(tptp_fun_B_3(A!8), A!8)),
% 1.93/1.47 inference(quant_inst,[status(thm)],[])).
% 1.93/1.47 tff(59,plain,
% 1.93/1.47 (element(tptp_fun_B_3(A!8), A!8)),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.93/1.47 tff(60,plain,
% 1.93/1.47 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(61,plain,
% 1.93/1.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[60])).
% 1.93/1.47 tff(62,plain,
% 1.93/1.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(63,plain,
% 1.93/1.47 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(64,plain,
% 1.93/1.47 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[63])).
% 1.93/1.47 tff(65,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 1.93/1.47 tff(66,plain,
% 1.93/1.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.93/1.47 tff(67,plain,
% 1.93/1.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.93/1.47 tff(68,plain,(
% 1.93/1.47 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(skolemize,[status(sab)],[67])).
% 1.93/1.47 tff(69,plain,
% 1.93/1.47 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.93/1.47 tff(70,plain,
% 1.93/1.47 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(71,plain,
% 1.93/1.47 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))),
% 1.93/1.47 inference(quant_inst,[status(thm)],[])).
% 1.93/1.47 tff(72,plain,
% 1.93/1.47 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.93/1.47 tff(73,plain,
% 1.93/1.47 (empty(A!8) | in(tptp_fun_B_3(A!8), A!8)),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 1.93/1.47 tff(74,plain,
% 1.93/1.47 (empty(A!8)),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[73, 53])).
% 1.93/1.47 tff(75,plain,
% 1.93/1.47 (^[A: $i, B: $i] : refl(((~empty(B)) | (A = B) | (~empty(A))) <=> ((~empty(B)) | (A = B) | (~empty(A))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(76,plain,
% 1.93/1.47 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[75])).
% 1.93/1.47 tff(77,plain,
% 1.93/1.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (A = B) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (A = B) | (~empty(A))))))), rewrite((~(~((~empty(B)) | (A = B) | (~empty(A))))) <=> ((~empty(B)) | (A = B) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (A = B) | (~empty(A)))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(78,plain,
% 1.93/1.47 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[77])).
% 1.93/1.47 tff(79,plain,
% 1.93/1.47 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(80,plain,
% 1.93/1.47 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 1.93/1.47 inference(bind,[status(th)],[])).
% 1.93/1.47 tff(81,plain,
% 1.93/1.47 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.93/1.47 inference(quant_intro,[status(thm)],[80])).
% 1.93/1.47 tff(82,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 1.93/1.47 tff(83,plain,
% 1.93/1.47 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.93/1.47 tff(84,plain,
% 1.93/1.47 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.93/1.47 tff(85,plain,(
% 1.93/1.47 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 1.93/1.47 inference(skolemize,[status(sab)],[84])).
% 1.93/1.47 tff(86,plain,
% 1.93/1.47 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[85, 78])).
% 1.93/1.47 tff(87,plain,
% 1.93/1.47 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[86, 76])).
% 1.93/1.47 tff(88,plain,
% 1.93/1.47 (~(A!8 = empty_set)),
% 1.93/1.47 inference(and_elim,[status(thm)],[33])).
% 1.93/1.47 tff(89,plain,
% 1.93/1.47 (empty(empty_set) <=> empty(empty_set)),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(90,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 1.93/1.47 tff(91,plain,
% 1.93/1.47 (empty(empty_set)),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.93/1.47 tff(92,plain,
% 1.93/1.47 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(93,plain,
% 1.93/1.47 (((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8))) <=> ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 1.93/1.47 inference(rewrite,[status(thm)],[])).
% 1.93/1.47 tff(94,plain,
% 1.93/1.47 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8))))),
% 1.93/1.47 inference(monotonicity,[status(thm)],[93])).
% 1.93/1.47 tff(95,plain,
% 1.93/1.47 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 1.93/1.47 inference(transitivity,[status(thm)],[94, 92])).
% 1.93/1.47 tff(96,plain,
% 1.93/1.47 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))),
% 1.93/1.47 inference(quant_inst,[status(thm)],[])).
% 1.93/1.47 tff(97,plain,
% 1.93/1.47 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8))),
% 1.93/1.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.93/1.47 tff(98,plain,
% 1.93/1.47 ($false),
% 1.93/1.47 inference(unit_resolution,[status(thm)],[97, 91, 88, 87, 74])).
% 1.93/1.47 % SZS output end Proof
%------------------------------------------------------------------------------